MATLAB: Triangulating fiducial marker position in c-arm image (DICOM) using stereoParameters

Computer Vision Toolboxdicomstereoparamterstriangulate

Hi,

I have 2 DICOM images exported from a c-arm imaging device. The images are 60 degrees apart in rotation and there is no translation between the two images. There is a marker in each image of which I would like to return the 3-D coordinates in world coordinate system.

The source-imager distance, pixel size, coordinates of the marker in each image, and angle between the two images are all known.

I'm attempting to use stereoParameters and triangulate to achieve this however I am unable to change the FocalLength parameter manually.

Is anyone able to assist me with this? Or recommend an alternative method to achieve my aim?

Regards, Joel

Best Answer

If you have the 3x4 projection matrices for the two gantry positions, then you can use the attached routine to do the triangulation. It isn't the optimal triangulation algorithm, but if your 2D localization errors are small, it serves most practical purposes.

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MATLAB: Stereo camera calibration and 3×4 camera matrices

Hi Tracy,

The functions in the Image Processing Toolbox and the Computer Vision System Toolbox use the pre-multiplication convention for coordinate transformations: row vectors mutiplied by a matrix. This is different from the convention you may see many textbooks, and it requires the matrix to be transposed. That is why you are seeing a 4x3 matrix instead of a 3x4 matrix. It does indeed map homogeneous world coordinates onto homogeneous image coordinates (ignoring distortion), but, again, it operates on row vectors.

[xw, yw, w] = [X,Y,Z,1] * P;

Now back to your problem. I would guess that the mismatch you are seeing happens because imagePoints come from the original image, which has some lens distortion. To do your test correctly, you have to first undistort the image, using the aptly named undistortImage function, and then detect the checkerboard in the undistorted image. Then you can compute the extrinsics and the camera matrix from the resulting image points.

By the way, in R2014b release the cameraParameters class has a pointsToWorld method, which maps image points to world points on a plane. And while I am at it, there is also a graphical app for stereo calibration.

MATLAB: How to calculate camera projection matrix

See this wiki link for some reading on composing the projection matrix from intrinsics and extrinsics.

Regarding what you've shown, I think the 640.2 in your intrinsic matrix is incorrect. If the SID is 1650 mm, then in pixels it would be 1650/.388 = 4252.6. Also, more information about the extrinsics is needed, in particular how your 2D image axes are initially oriented in the first view relative to the 3D world x,y,z axes. The 90 degree rotation matrix alone does not provide this information. That just tells us how the axes change between views.

I give a solution to your triangulation example in my response to your earlier post, under some assumptions on the missing extrinsics. Note that my matrix conventions, and the conventions of the above wiki link, are different than the Computer Vision Toolbox's. I always work with upper triangular intrinsic matrices, whereas the toolbox seems to transpose everything and make it lower triangular.

Best Answer

Related Solutions

MATLAB: Stereo camera calibration and 3×4 camera matrices

MATLAB: How to calculate camera projection matrix

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